Shipping with the Square Store is very basic as you know and doesn't work for all businesses. If for example don't charge shipping because I can put it in an envelope. That doesn't work for everyone.
Here are a couple of options
Create a flat rate that you know you can get most of your products out in. USPS flat rate box is $X and I can get X in it. Then if larger items require a larger box you adjust those items only.
Check out addon app Shipstation.
Upgrade to an e-commerce option that fits your needs better.
